1. What is the Chi-Square Goodness of Fit Test?

The Chi-Square (χ²) Goodness of Fit test determines whether observed frequency counts differ significantly from expected counts. It's commonly used to test if a sample comes from a population with a specific distribution.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

Where:

• \( O \) — Observed count
• \( E \) — Expected count
• \( \sum \) — Sum over all categories

Explanation: The test compares observed values with expected values under the null hypothesis. Large χ² values indicate poor fit between observed and expected distributions.

3. Importance of Chi-Square Test

Details: The test is widely used in genetics, marketing research, quality control, and other fields to test hypotheses about distributions.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values. Expected counts should not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the test?
A: The test assumes random sampling, independence of observations, and expected counts ≥5 for most categories.

Q2: How do I interpret the χ² value?
A: Compare your χ² value to critical values from the chi-square distribution table with (k-1) degrees of freedom (k = number of categories).

Q3: What's the difference between goodness of fit and test of independence?
A: Goodness of fit compares observed to expected counts for one variable, while test of independence examines relationship between two variables.

Q4: Can I use this for small sample sizes?
A: For small samples (expected counts <5), consider Fisher's exact test or combine categories.

Q5: How does this relate to TI-83 Plus?
A: The TI-83 Plus can perform this test using the χ²GOF-Test function in the STAT TESTS menu.